Verified answer

Q: √12 / (2√2)

Multiply by √2 / √2 to the fraction

= √12(√2) / 2(√2)(√2)

= √24 / 4

Simplify √24

√24 = √4 × √6 = 2√6

The fraction becomes

= 2√6 / 4

Divide the fraction by 2/2

= √6 / 2

The simpliest form is √6 / 2

Rationalize the denominator by multiplying it by itself. Then we get this:

√12 / 2√2 =

(√12 / 2√2)∙(2√2 / 2√2) =

2√(2∙12) / (2√2)² =

2√24 / (4∙2) = 2√(4∙6) / 8 =

(2∙2)√6 / 8 =

4√6 / 8 =

(√6) / 2 ≈

1.2247.

The answer can be proved by simply performing the division in the original expression and in the simplified expression, then comparing the two results. If they are the same, then our simplified expression is correct. This answer checks out. The other answers also work, because √(3/2) = √1.5 ≈ 1.2247.

First you want to get the square root out of the denominator so mutiply the top and bottom by square root 2

square root 12 * square root 2 / 2 * square root 2 * square root 2

square root 24 / 2 * square root 4

square root 24 / 2 * 2

square root 24 / 4

square root 4 * square root 6 / 4

2 * square root 6 / 4

square root 3 / 2

Sqrt(12)=2sqrt(3)/2sqrt(2)=sqrt(3/2) answer.

sqrt(6)/2